Research Article: State-Space Analysis of Time-Varying Higher-Order Spike Correlation for Multiple Neural Spike Train Data

Date Published: March 8, 2012

Publisher: Public Library of Science

Author(s): Hideaki Shimazaki, Shun-ichi Amari, Emery N. Brown, Sonja Grün, Olaf Sporns

Abstract: Precise spike coordination between the spiking activities of multiple neurons is suggested as an indication of coordinated network activity in active cell assemblies. Spike correlation analysis aims to identify such cooperative network activity by detecting excess spike synchrony in simultaneously recorded multiple neural spike sequences. Cooperative activity is expected to organize dynamically during behavior and cognition; therefore currently available analysis techniques must be extended to enable the estimation of multiple time-varying spike interactions between neurons simultaneously. In particular, new methods must take advantage of the simultaneous observations of multiple neurons by addressing their higher-order dependencies, which cannot be revealed by pairwise analyses alone. In this paper, we develop a method for estimating time-varying spike interactions by means of a state-space analysis. Discretized parallel spike sequences are modeled as multi-variate binary processes using a log-linear model that provides a well-defined measure of higher-order spike correlation in an information geometry framework. We construct a recursive Bayesian filter/smoother for the extraction of spike interaction parameters. This method can simultaneously estimate the dynamic pairwise spike interactions of multiple single neurons, thereby extending the Ising/spin-glass model analysis of multiple neural spike train data to a nonstationary analysis. Furthermore, the method can estimate dynamic higher-order spike interactions. To validate the inclusion of the higher-order terms in the model, we construct an approximation method to assess the goodness-of-fit to spike data. In addition, we formulate a test method for the presence of higher-order spike correlation even in nonstationary spike data, e.g., data from awake behaving animals. The utility of the proposed methods is tested using simulated spike data with known underlying correlation dynamics. Finally, we apply the methods to neural spike data simultaneously recorded from the motor cortex of an awake monkey and demonstrate that the higher-order spike correlation organizes dynamically in relation to a behavioral demand.

Partial Text: Precise spike coordination within the spiking activities of multiple single neurons is discussed as an indication of coordinated network activity in the form of cell assemblies [1] comprising neuronal information processing. Possible theoretical mechanisms and conditions for generating and maintaining such precise spike coordination have been proposed on the basis of neuronal network models [2]–[4]. The effect of synchronous spiking activities on downstream neurons has been theoretically investigated and it was demonstrated that these are more effective in generating output spikes [5]. Assembly activity was hypothesized to organize dynamically as a result of sensory input and/or in relation to behavioral context [6]–[10]. Supportive experimental evidence was provided by findings of the presence of excess spike synchrony occurring dynamically in relation to stimuli [11]–[14], behavior [14]–[19], or internal states such as memory retention, expectation, and attention [8], [20]–[23].

In this study, we introduced a novel method for estimating dynamic spike interactions in multiple parallel spike sequences by means of a state-space analysis (see Methods for details). By applying this method to nonstationary spike train data using the pairwise log-linear model, we can extend the stationary analysis of the spike train data by the Ising/spin-glass model to within-trial nonstationary analysis (Figure 3). In addition, our approach is not limited to a pairwise analysis, but can perform analyses of time-varying higher-order spike interactions (Figure 4). It has been discussed whether higher-order spike correlations are important to characterize neuronal population spiking activities, assuming stationarity in the spike data [54]–[59]. Based on the state-space model optimized by our algorithm, we developed two methods to validate and test its latent spike interaction parameters, in particular the higher-order interaction parameters, which may dynamically change within an experimental trial. In the first method, we selected the proper order for the spike interactions incorporated in the model under the model selection framework using the approximate formula of the AIC for this state-space model (In Methods, ‘Selection of state-space model by information criteria’). This method selects the model that best fits the data overall across the entire observation period. The selected model can then be used to visualize the dynamic spike interactions or for a performance comparison with other statistical models of neuronal spike data. However, more importantly, the detailed structure of the transient higher-order spike interactions needs to be tested locally in time, particularly in conjunction with the behavioral paradigm. To meet this goal, we combined the Bayesian model comparison method (the Bayes factor) with a surrogate method (In Methods, ‘Bayesian model comparison method for detecting spike correlation’). The method allows us to test for the presence of higher-order spike correlations and examine its relations to experimentally relevant events. We demonstrated the utility of the method using neural spike train data simultaneously recorded from primary motor cortex of an awake monkey. The result is consistent with, and further extended the findings in the previous report [8]: We detected an increase in triple-wise spike interaction among three neurons in the motor cortex during the preparatory period in a delayed motor task, which was also tightly locked to the expected signals. Although the analysis was done for a limited number of neurons, smaller than the expected size of an assembly, it demonstrates that the nonstationary analysis of the higher-order activities is useful to reveal cooperative activities of the neurons that are organized in relation to behavioral demand. Of course, further analysis is required to strengthen the findings made above including a meta-analysis of many different sets of multiple neurons recorded under the same conditions.